[Solved] MATH307 Group Homework11

Instructions: Read textbook pages 135 to 142 before working on the homework problems. Show all steps to get full credits.

0 1 0

1. Find the determinants of the following matrices: A = 1 0 0 (a per-

0 0 1

1 0 0

mutation elementary row operation matrix), B = 0 3 0 (a multipli-

0 0 1 1 0 0

cation elementary row operation matrix), C = 1 1 0 (an adding a

• 0 1

multiple of one row to another row elementary row operation matrix), D =

2 0 0 1 4 1

• 5 0 ,E = 1 1 0 .

0 0 3 2 0 1

2. Let A be an invertible matrix, one can prove that |A| 6= 0, find the determinant of A¹ in terms of |A|.
3. If |A| = 2,|B| = 1, find |A¹(B^T)²|,|(B^T)¹A³|.
4. Suppose that Q is a n n real orthonormal matrix, i.e., QQ^T = I. Find the possible values for |Q|.